The study found, for instance, that about 8 percent of children
born in the early 1980s who grew up in families in the bottom
fifth of the income distribution managed to reach the top fifth
for their age group today. The rate was nearly identical for
children born a decade earlier.

Among children born into the middle fifth of the income
distribution, about 20 percent climbed into the top fifth as
adults, also largely unchanged over the last decade.

Things haven't gotten worse, but one of the study's
authors told the Times that the odds of escaping poverty are only
half as high in the U.S. as in highest-ranked countries for
mobility such as Denmark.

"Although rank-based measures of mobility remained stable, income
inequality increased substantially over the period we
study,"
according to the study. "Hence, the consequences of the
'birth lottery' – the parents to whom a child is born – are
larger today than in the past."

This
visualization from the study shows how the "rungs" of the
income ladder have grown further apart (that's inequality at
work) but a child's chance at actually climbing those rungs
hasn't changed.